Nuprl Lemma : pv11_p1-ilf
(∀[loc:Id]. ∀[accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[mf:pv11_p1_headers_type{i:l}(Cmd)].
∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc) o pv11_p1_p1b'base(Cmd;mf)) o
pv11_p1_ScoutState(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc))(e)
⇐⇒ ((header(e) = ``pv11_p1 p1b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id
× pv11_p1_Ballot_Num()
× pv11_p1_Ballot_Num()
× ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((pv11_p1_init_ballot_num() loc) = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num())
∧ (d = 0 ∈ ℤ)
∧ (i = loc(e) ∈ Id)
∧ (↓(((pv11_p1_init_ballot_num() loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(fst(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_init_ballot_num() loc;es;e))) < pv11_p1_threshold(accpts)
∧ (m
= make-Msg(``pv11_p1 adopted``;<pv11_p1_init_ballot_num() loc
, snd(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_init_ballot_num()
loc;es;e))
>)
∈ Message(mf)))
∨ ((¬((pv11_p1_init_ballot_num() loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (m = make-Msg(``pv11_p1 preempted``;fst(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[z3:ℤ]. ∀[z1:pv11_p1_Ballot_Num()]. ∀[reps,accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[z4:Cmd].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_commander_output(Cmd;accpts;reps;mf) <z1, z3, z4> o pv11_p1_p2b'base(Cmd;mf)) o pv11_p1_Comm\000CanderState(Cmd;accpts;mf) z1 z3)(e)
⇐⇒ ((header(e) = ``pv11_p1 p2b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()))
∧ ((z1 = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num()) ∧ (z3 = (fst(snd(snd(msgval(e))))) ∈ ℤ))
∧ (d = 0 ∈ ℤ)
∧ (↓((z1 = (snd(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(pv11_p1_CommanderStateFun(Cmd;accpts;mf;z1;z3;es;e)) < pv11_p1_threshold(accpts)
∧ i ↓∈ reps
∧ (m = make-Msg([decision];<z3, z4>) ∈ Message(mf)))
∨ ((¬(z1 = (snd(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (i = loc(e) ∈ Id)
∧ (m = make-Msg(``pv11_p1 preempted``;snd(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[loc:Id]. ∀[param:pv11_p1_Ballot_Num()]. ∀[accpts:bag(Id)]. ∀[Cmd:{T:Type| valueall-type(T)} ].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_upd_bnum() param loc) o pv11_p1_p1b'base(Cmd;mf)) o
pv11_p1_ScoutState(Cmd;accpts;mf) (pv11_p1_upd_bnum() param loc))(e)
⇐⇒ ((header(e) = ``pv11_p1 p1b`` ∈ Name)
∧ has-es-info-type(es;e;mf;Id
× pv11_p1_Ballot_Num()
× pv11_p1_Ballot_Num()
× ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((pv11_p1_upd_bnum() param loc) = (fst(snd(msgval(e)))) ∈ pv11_p1_Ballot_Num())
∧ (d = 0 ∈ ℤ)
∧ (i = loc(e) ∈ Id)
∧ (↓(((pv11_p1_upd_bnum() param loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num())
∧ #(fst(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_upd_bnum() param
loc;es;e))) < pv11_p1_threshold(accpts)
∧ (m
= make-Msg(``pv11_p1 adopted``;<pv11_p1_upd_bnum() param loc
, snd(pv11_p1_ScoutStateFun(Cmd;accpts;mf;pv11_p1_upd_bnum() param
loc;es;e))
>)
∈ Message(mf)))
∨ ((¬((pv11_p1_upd_bnum() param loc) = (fst(snd(snd(msgval(e))))) ∈ pv11_p1_Ballot_Num()))
∧ (m = make-Msg(``pv11_p1 preempted``;fst(snd(snd(msgval(e))))) ∈ Message(mf))))})
∧ (∀[Cmd:{T:Type| valueall-type(T)} ]. ∀[accpts,ldrs:bag(Id)]. ∀[ldrs_uid:Id ─→ ℤ]. ∀[reps:bag(Id)].
∀[mf:pv11_p1_headers_type{i:l}(Cmd)]. ∀[es:EO+(Message(mf))]. ∀[e:E]. ∀[d:ℤ]. ∀[i:Id]. ∀[m:Message(mf)].
{<d, i, m> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf)(e)
⇐⇒ ↓(loc(e) ↓∈ ldrs
∧ ((((((d = 0 ∈ ℤ) ∧ (m = make-Msg(``pv11_p1 p1a``;<loc(e), pv11_p1_init_ballot_num() loc(e)>) ∈ Message(mf)) \000C∧ i ↓∈ accpts)
∧ (↑first(e)))
∨ ((no ((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc(e)) o
pv11_p1_p1b'base(Cmd;mf)) o pv11_p1_ScoutState(Cmd;accpts;mf)
(pv11_p1_init_ballot_num() loc(e))) prior to e)
∧ <d, i, m> ∈ {((pv11_p1_scout_output(Cmd;accpts;mf) (pv11_p1_init_ballot_num() loc(e)) o
pv11_p1_p1b'base(Cmd;mf)) o pv11_p1_ScoutState(Cmd;accpts;mf)
(pv11_p1_init_ballot_num() loc(e)))}(e)))
∨ (∃e':{e':E| e' ≤loc e }
∃z1:pv11_p1_Ballot_Num()
∃z3:ℤ
∃z4:Cmd
(((((header(e') = [propose] ∈ Name) ∧ has-es-info-type(es;e';mf;ℤ × Cmd))
∧ ((↑(fst(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e')))))
∧ (¬↑(pv11_p1_in_domain(Cmd) (fst(msgval(e')))
(snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e')))))))
∧ (z1 = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e'))) ∈ pv11_p1_Ballot_Num())
∧ (<z3, z4> = msgval(e') ∈ (ℤ × Cmd)))
∨ (((header(e') = ``pv11_p1 adopted`` ∈ Name)
∧ has-es-info-type(es;e';mf;pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)))
∧ ((fst(msgval(e'))) = (fst(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e'))) ∈ pv11_p1_Ballot_Num())
∧ ((<z3, z4> ↓∈ snd(snd(pv11_p1_LeaderStateFun(Cmd;ldrs_uid;...;...;...))) ∧ ...) ∨ ...)
∧ ...))
∧ ...)))
∨ ...))
∨ ...})
Proof
Definitions occuring in Statement :
pv11_p1_main: pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;mf),
pv11_p1_LeaderStateFun: pv11_p1_LeaderStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_scout_output: pv11_p1_scout_output(Cmd;accpts;mf),
pv11_p1_ScoutStateFun: pv11_p1_ScoutStateFun(Cmd;accpts;mf;x;es;e),
pv11_p1_ScoutState: pv11_p1_ScoutState(Cmd;accpts;mf),
pv11_p1_commander_output: pv11_p1_commander_output(Cmd;accpts;reps;mf),
pv11_p1_CommanderStateFun: pv11_p1_CommanderStateFun(Cmd;accpts;mf;x;zzs;es;e),
pv11_p1_CommanderState: pv11_p1_CommanderState(Cmd;accpts;mf),
pv11_p1_AcceptorStateFun: pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;mf;es;e),
pv11_p1_init_ballot_num: pv11_p1_init_ballot_num(),
pv11_p1_p2b'base: pv11_p1_p2b'base(Cmd;mf),
pv11_p1_p1b'base: pv11_p1_p1b'base(Cmd;mf),
pv11_p1_threshold: pv11_p1_threshold(accpts),
pv11_p1_in_domain: pv11_p1_in_domain(Cmd),
pv11_p1_pmax: pv11_p1_pmax(Cmd;ldrs_uid),
pv11_p1_headers_type: pv11_p1_headers_type{i:l}(Cmd),
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_upd_bnum: pv11_p1_upd_bnum(),
pv11_p1_is_bnum: pv11_p1_is_bnum(),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
msg-interface: Interface,
make-Msg: make-Msg(hdr;val),
es-info-body: msgval(e),
has-es-info-type: has-es-info-type(es;e;f;T),
es-header: header(e),
Message: Message(f),
eclass2: (X o Y),
eclass1: (f o X),
no-classrel-in-interval: (no X between start and e),
no-prior-classrel: (no X prior to e),
classrel: v ∈ X(e),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
name: Name,
l_member: (x ∈ l),
cons: [a / b],
nil: [],
list: T List,
valueall-type: valueall-type(T),
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
guard: {T},
pi1: fst(t),
pi2: snd(t),
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
token: "$token",
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag-size: #(bs),
bag: bag(T)
Lemmas :
sq_stable__and,
equal_wf,
cons_wf_listp,
nil_wf,
listp_wf,
vatype_wf,
cons_wf,
pv11_p1_Ballot_Num_wf,
list_wf,
equal-wf-T-base,
sq_stable__equal,
squash_wf,
int_seg_wf,
length_wf,
name_wf,
pv11_p1_headers_wf,
l_all_iff,
l_member_wf,
pv11_p1_headers_fun_wf,
cons_member,
equal-wf-base,
iff_weakening_equal,
classrel_wf,
msg-interface_wf,
eclass2_wf,
eclass1_wf,
bag_wf,
pv11_p1_p1b'base_wf,
pv11_p1_scout_output_wf,
pv11_p1_init_ballot_num_wf,
pv11_p1_ScoutState_wf,
make-msg-interface_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Message_wf,
subtype_rel_dep_function,
pv11_p1_headers_type_wf,
valueall-type_wf,
Id_wf,
iff_transitivity,
iff_weakening_uiff,
eclass2-eclass1-classrel,
base-classrel-equal,
subtype_rel_weakening,
ext-eq_weakening,
pv11_p1_ScoutState-classrel,
has-es-info-type_wf,
es-info-body_wf,
pv11_p1_ScoutStateFun_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
es-header_wf,
bag-member-spread-to-pi,
bag-member-ifthenelse,
empty-bag_wf,
pv11_p1_eq_bnums_wf,
ifthenelse_functionality_wrt_iff,
false_wf,
bag-member-empty-weak,
bag-member-single-weak,
single-bag_wf,
pv11_p1_adopted'send_wf,
ifthenelse-false-right,
bool_wf,
eqtt_to_assert,
pv11_p1_eq_bnums-assert,
lt_int_wf,
bag-size_wf,
nat_wf,
pv11_p1_threshold_wf,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
pv11_p1_preempted'send_wf,
assert_wf,
sq_stable__has-es-info-type,
squash-assert,
member_wf,
int_subtype_base,
make-Msg_wf,
pi1_wf_top,
bool_cases,
not_wf,
true_wf,
or_wf,
pv11_p1_p2b'base_wf,
pv11_p1_commander_output_wf,
pv11_p1_CommanderState_wf,
pv11_p1_CommanderState-classrel,
pv11_p1_CommanderStateFun_wf,
pv11_p1_decision'broadcast_wf,
bag-member-map,
eq_int_wf,
assert_of_eq_int,
assert_of_band,
equal-wf-base-T,
mk-msg-interface_wf,
sq_stable__bag-member,
pv11_p1_upd_bnum_wf,
pv11_p1_main_wf,
parallel-classrel-weak,
class-at_wf,
pv11_p1_Leader_wf,
pv11_p1_Acceptor_wf,
classrel-at,
parallel-class_wf,
pv11_p1_SpawnFirstScout_wf,
bind-class_wf,
pv11_p1_LeaderPropose_wf,
pv11_p1_LeaderAdopted_wf,
pv11_p1_Commander_wf,
pv11_p1_LeaderPreempted_wf,
pv11_p1_Scout_wf,
on-loc-classrel,
pv11_p1_mk_bnum_wf,
bind-class-rel-weak,
pv11_p1_leader_propose_wf,
pv11_p1_propose'base_wf,
pv11_p1_LeaderState_wf,
pv11_p1_LeaderState-classrel,
pv11_p1_LeaderStateFun_wf,
pv11_p1_leader_adopted_wf,
pv11_p1_adopted'base_wf,
pv11_p1_CommanderNotify_wf,
pv11_p1_CommanderOutput_wf,
eo-forward_wf,
return-loc-bag-class-classrel,
pv11_p1_p2a'broadcast_wf,
pair-eta,
once-classrel-weak,
pv11_p1_leader_preempted_wf,
pv11_p1_preempted'base_wf,
pv11_p1_ScoutNotify_wf,
pv11_p1_ScoutOutput_wf,
pv11_p1_p1a'broadcast_wf,
pv11_p1_AcceptorsP1a_wf,
pv11_p1_AcceptorsP2a_wf,
pv11_p1_p1b'send_wf,
pv11_p1_p1a'base_wf,
pv11_p1_AcceptorState_wf,
pv11_p1_AcceptorState-classrel,
pv11_p1_AcceptorStateFun_wf,
pv11_p1_p2b'send_wf,
pv11_p1_p2a'base_wf,
member-eo-forward-E,
es-first_wf2,
no-prior-classrel_wf,
sq_or_wf,
es-le_wf,
list-subtype-bag,
map_wf,
bag-member-append,
bag-member-filter,
bnot_wf,
bl-exists_wf,
pv11_p1_in_domain_wf,
assert_of_bnot,
pv11_p1_update_proposals_wf,
pv11_p1_pmax_wf,
pv11_p1_lt_bnum_wf,
filter_wf5,
pv11_p1_is_bnum_wf,
and_wf,
assert-name_eq,
assert-bl-exists,
l_exists_wf,
l_exists_iff,
eo-forward-loc,
eo-forward-first2,
eo-forward-no-prior-classrel,
no-classrel-in-interval_wf,
es-info-type_wf,
subtype_rel_product,
top_wf,
subtype_top,
subtype_rel_transitivity,
es-le-loc,
decidable__es-le
Latex:
(\mforall{}[loc:Id]. \mforall{}[accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc))(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p1b``)
\mwedge{} has-es-info-type(es;e;mf;Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(msgval(e)))))
\mwedge{} (d = 0)
\mwedge{} (i = loc(e))
\mwedge{} (\mdownarrow{}(((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(snd(msgval(e))))))
\mwedge{} \#(fst(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;pv11\_p1\_init\_ballot\_num()
loc;es;e))) < pv11\_p1\_threshold(accpts)
\mwedge{} (m
= make-Msg(``pv11\_p1 adopted``;<pv11\_p1\_init\_ballot\_num() loc
, snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;...
loc;es;e))
>)))
\mvee{} ((\mneg{}((pv11\_p1\_init\_ballot\_num() loc) = (fst(snd(snd(msgval(e)))))))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;fst(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[z3:\mBbbZ{}]. \mforall{}[z1:pv11\_p1\_Ballot\_Num()]. \mforall{}[reps,accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[z4:Cmd]. \mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_commander\_output(Cmd;accpts;reps;mf)
<z1, z3, z4> o pv11\_p1\_p2b'base(Cmd;mf)) o
pv11\_p1\_CommanderState(Cmd;accpts;mf) z1 z3)(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p2b``)
\mwedge{} has-es-info-type(es;e;mf;Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()))
\mwedge{} ((z1 = (fst(snd(msgval(e))))) \mwedge{} (z3 = (fst(snd(snd(msgval(e)))))))
\mwedge{} (d = 0)
\mwedge{} (\mdownarrow{}((z1 = (snd(snd(snd(msgval(e))))))
\mwedge{} \#(pv11\_p1\_CommanderStateFun(Cmd;accpts;mf;z1;z3;es;e)) < pv11\_p1\_threshold(accpts)
\mwedge{} i \mdownarrow{}\mmember{} reps
\mwedge{} (m = make-Msg([decision];<z3, z4>)))
\mvee{} ((\mneg{}(z1 = (snd(snd(snd(msgval(e)))))))
\mwedge{} (i = loc(e))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;snd(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[loc:Id]. \mforall{}[param:pv11\_p1\_Ballot\_Num()]. \mforall{}[accpts:bag(Id)]. \mforall{}[Cmd:\{T:Type| valueall-type(T)\} ].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_upd\_bnum() param loc) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_upd\_bnum() param loc))(e)
\mLeftarrow{}{}\mRightarrow{} ((header(e) = ``pv11\_p1 p1b``)
\mwedge{} has-es-info-type(es;e;mf;Id
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} pv11\_p1\_Ballot\_Num()
\mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)))
\mwedge{} ((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(msgval(e)))))
\mwedge{} (d = 0)
\mwedge{} (i = loc(e))
\mwedge{} (\mdownarrow{}(((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(snd(msgval(e))))))
\mwedge{} \#(fst(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;pv11\_p1\_upd\_bnum() param
loc;es;e))) < pv11\_p1\_threshold(accpts)
\mwedge{} (m
= make-Msg(``pv11\_p1 adopted``;<pv11\_p1\_upd\_bnum() param loc
, snd(pv11\_p1\_ScoutStateFun(Cmd;accpts;mf;...
param
loc;es;e))
>)))
\mvee{} ((\mneg{}((pv11\_p1\_upd\_bnum() param loc) = (fst(snd(snd(msgval(e)))))))
\mwedge{} (m = make-Msg(``pv11\_p1 preempted``;fst(snd(snd(msgval(e))))))))\})
\mwedge{} (\mforall{}[Cmd:\{T:Type| valueall-type(T)\} ]. \mforall{}[accpts,ldrs:bag(Id)]. \mforall{}[ldrs$_{uid}$:Id\000C {}\mrightarrow{} \mBbbZ{}]. \mforall{}[reps:bag(Id)].
\mforall{}[mf:pv11\_p1\_headers\_type\{i:l\}(Cmd)]. \mforall{}[es:EO+(Message(mf))]. \mforall{}[e:E]. \mforall{}[d:\mBbbZ{}]. \mforall{}[i:Id].
\mforall{}[m:Message(mf)].
\{<d, i, m> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid}$;reps;mf)(e)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}(loc(e) \mdownarrow{}\mmember{} ldrs
\mwedge{} ((((((d = 0) \mwedge{} (m = make-Msg(``pv11\_p1 p1a``;<loc(e), pv11\_p1\_init\_ballot\_num() loc(e)>)\000C) \mwedge{} i \mdownarrow{}\mmember{} accpts)
\mwedge{} (\muparrow{}first(e)))
\mvee{} ((no ((pv11\_p1\_scout\_output(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc(e)) o
pv11\_p1\_p1b'base(Cmd;mf)) o pv11\_p1\_ScoutState(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc(e))) prior to e)
\mwedge{} <d, i, m> \mmember{} \{((pv11\_p1\_scout\_output(Cmd;accpts;mf)
(pv11\_p1\_init\_ballot\_num() loc(e)) o pv11\_p1\_p1b'base(Cmd;mf)) o
pv11\_p1\_ScoutState(Cmd;accpts;mf) (pv11\_p1\_init\_ballot\_num() loc(e)))\}(
e)))
\mvee{} (\mexists{}e':\{e':E| e' \mleq{}loc e \}
\mexists{}z1:pv11\_p1\_Ballot\_Num()
\mexists{}z3:\mBbbZ{}
\mexists{}z4:Cmd
(((((header(e') = [propose]) \mwedge{} has-es-info-type(es;e';mf;\mBbbZ{} \mtimes{} Cmd))
\mwedge{} ((\muparrow{}(fst(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;es;e\000C')))))
\mwedge{} (\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) (fst(msgval(e')))
(snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;e\000Cs;e')))))))
\mwedge{} (z1 = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}$;mf;es;e'\000C))))
\mwedge{} (<z3, z4> = msgval(e')))
\mvee{} (((header(e') = ``pv11\_p1 adopted``)
\mwedge{} has-es-info-type(es;e';mf;pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num()
\mtimes{} \mBbbZ{}
\mtimes{} Cmd) List)))
\mwedge{} ((fst(msgval(e'))) = (fst(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid\mbackslash{}f\000Cf7d$;mf;es;e'))))
\mwedge{} ((<z3, z4> \mdownarrow{}\mmember{} snd(snd(pv11\_p1\_LeaderStateFun(Cmd;ldrs$_{uid}\mbackslash{}\000Cff24;mf;es;e')))
\mwedge{} (\mneg{}(\mexists{}p2:Cmd. (<z3, p2> \mmember{} pv11\_p1\_pmax(Cmd;ldrs$_{uid}$) \000C(snd(msgval(e')))))))
\mvee{} (\mexists{}v2:pv11\_p1\_Ballot\_Num()
(<v2, z3, z4> \mdownarrow{}\mmember{} snd(msgval(e'))
\mwedge{} (\mneg{}(\mexists{}z5:pv11\_p1\_Ballot\_Num(). \mexists{}z8:Cmd. ((\muparrow{}(v2 ... ...)) \mwedge{} ...))))))
\mwedge{} ...))
\mwedge{} ...)))
\mvee{} ...))
\mvee{} ...\})
Date html generated:
2015_07_23-PM-04_41_26
Last ObjectModification:
2015_02_04-AM-08_58_16
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